I have had an interesting experience in regard to this. My graduate program at the University of Wisconsin-Madison has actually been incredibly flexible with the areas of research that I want to pursue. The program generally consists of just coursework, however I have been able to do pretty much whatever I want on the side (research).
With this freedom, myself and another graduate student began our own laboratory within the department that focuses on medical technology for developing countries. We have been able to convince undergraduate students, as well as graduate students to work within our lab for free. We have also set up an internship program, where students outside of the university can join. Our professor was also happy to put his name on grant applications for our project.
In my experience there are two types of potential professors. First the ones that are interested in their own research - in which case you are required to do something for them. Or the other (old skool) professors who think you should go about getting your degree on your own. The problem is this second type generally does not come with any type of funding.
My overall advice would be to pursue graduate school, especially if you need for time to work on your idea. Graduate schools have excellent resources to help you with your company (especially within this economy).
P.S. I'm actually involved in a start-up company right now while attending school. Perfect opportunity to incubate your idea while you wait to develop.